Abstract
Sparse representation is a signal model to represent signals with a linear combination of a small number of prototype signals called atoms, and a set of atoms is called a dictionary. The design of the dictionary is a fundamental problem for sparse representation. However, when there are scaled or translated features in the signals, unstructured dictionary models cannot extract such features. In this paper, we propose a structured dictionary model which is scale and shift-invariant to extract features which commonly appear in several scales and locations. To achieve both scale and shift invariance, we assume that atoms of a dictionary are generated from vectors called ancestral atoms by scaling and shift operations, and an algorithm to learn these ancestral atoms is proposed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc. B 58, 267–288 (1994)
Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)
Hastie, T., Tibshirani, R., Wainwright, M.: Statistical Learning with Sparsity: The Lasso and Generalizations. Chapman & Hall/CRC, Boca Raton (2015)
Olshausen, B.A., et al.: Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381(6583), 607–609 (1996)
Engan, K., Aase, S.O., Husoy, J.H.: Method of optimal directions for frame design. In: 1999 Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, pp. 2443–2446 (1999)
Aharon, M., Elad, M., Bruckstein, A.: K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Sig. Process. 54(11), 4311–4322 (2006)
Mairal, J., Bach, F., Ponce, J., Sapiro, G.: Online dictionary learning for sparse coding. In: Proceedings of the 26th Annual International Conference on Machine Learning, ICML 2009, pp. 689–696. ACM, New York (2009)
Barzideh, F., Skretting, K., Engan, K.: Imposing shift-invariance using flexible structure dictionary learning (FSDL). Digit. Sig. Proc. 69, 162–173 (2017)
Mairal, J., Sapiro, G., Elad, M.: Learning multiscale sparse representations for image and video restoration. Multiscale Model. Simul. 7(1), 214–241 (2008)
Shen, Y., Xiong, H., Dai, W.: Multiscale dictionary learning for hierarchical sparse representation. In: 2017 IEEE International Conference on Multimedia and Expo (ICME), pp. 1332–1337, July 2017
Grandits, T., Pock, T.: Optimizing wavelet bases for sparser representations. In: Pelillo, M., Hancock, E. (eds.) EMMCVPR 2017. LNCS, vol. 10746, pp. 249–262. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78199-0_17
Olshausen, B.A., Sallee, P., Lewicki, M.S.: Learning sparse image codes using a wavelet pyramid architecture. In: Advances in Neural Information Processing Systems, NIPS 2000, Denver, CO, USA, vol. 13, pp. 887–893 (2000)
Aritake, T., Hino, H., Murata, N.: Learning ancestral atom via sparse coding. IEEE J. Sel. Top. Sig. Process. 7(4), 586–594 (2013)
Zheng, G., Yang, Y., Carbonell, J.: Efficient shift-invariant dictionary learning. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2016, pp. 2095–2104. ACM, New York (2016)
Daugman, J.G.: Two-dimensional spectral analysis of cortical receptive field profiles. Vis. Res. 20(10), 847–856 (1980)
Acknowledgement
This work was supported by JST CREST Grant Number JPMJCR1761 and JSPS KAKENHI Grant Numbers JP17H01793, JP18H03291.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Aritake, T., Murata, N. (2019). Learning Scale and Shift-Invariant Dictionary for Sparse Representation. In: Nicosia, G., Pardalos, P., Umeton, R., Giuffrida, G., Sciacca, V. (eds) Machine Learning, Optimization, and Data Science. LOD 2019. Lecture Notes in Computer Science(), vol 11943. Springer, Cham. https://doi.org/10.1007/978-3-030-37599-7_39
Download citation
DOI: https://doi.org/10.1007/978-3-030-37599-7_39
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-37598-0
Online ISBN: 978-3-030-37599-7
eBook Packages: Computer ScienceComputer Science (R0)